What’s so unusual is that not even the colleges themselves know the answer. But the parlor game is afoot, with only one real clue: So far, all the colleges are led by women.

Coincidence? Unlikely. With about 23 percent of U.S. college presidents women, the odds of a dozen randomly selected institutions all having female leaders are 1 in 50 million.

Melissa Berman, president and CEO of Rockefeller Philanthropy Advisors in New York, thinks the donor might be “a woman who maybe grew up in an era in which the opportunity to go to college was not taken for granted by women, and who feels that women in leadership positions are important motivators for women to be able to achieve their potential.”

Brian O’Rourke, director of development at Clemson University in South Carolina, imagines “a group of high-powered women that want to make sure women presidents in higher education are successful.”

“My gut tells me it’s a group of people sitting around saying, `Let’s just make a huge difference,”‘ he said. (Clemson has not gotten a contribution from the mystery donor.)

The gifts, ranging from $1 million to perhaps $10 million, and totaling up to $68.5 million so far, have arrived over the past seven weeks in similarly secretive fashion at colleges around the country, including Purdue in Indiana, Montclair State in New Jersey, and the University of Southern Mississippi. All were contacted by a law firm or other intermediary and given a highly unusual condition: College officials had to promise – in writing, in some cases – not to try to find out the donor’s identity.

The donations arrived the form of in cashier’s checks, or checks from law firms or other intermediaries. In most cases, the donor specified that the money be used for financial aid.

Michigan State University, which has a woman president, may be the 13th and latest recipient, announcing Thursday that it has been given an anonymous $10 million.

Philanthropy experts are thrilled but flummoxed. None knew of donors who had previously singled out colleges led by women. None could think of anything else the schools have in common.

“It could be this person wants to support female leaders of institutions of higher ed, but one then starts wondering why these and not others,” said Dennis Cross, vice president of university advancement at Washington & Lee University in Virginia, which is not one of the lucky recipients.

A few theories have popped up on Web sites, including talk show host Oprah Winfrey and someone connected with disgraced financier Bernie Madoff.

A spokeswoman for Winfrey said she was not the source. A representative for real estate baroness Leona Helmsley’s estate, which gave away $136 million Tuesday to hospitals, foundations and the homeless, also denied involvement.

As for whether the donor is someone scandalous trying to hide his identity, and perhaps not embarrass the colleges, New York University law professor Harvey Dale said that’s possible, but it doesn’t fit the personality type of most crooks.

Colleges, Dale said, are generally not required to do deep due diligence on gifts, though in this case at least one college checked with Homeland Security and the IRS to make sure it wasn’t dirty money.

The most plausible scenario seems to be that the money is coming from a “giving circle,” where a group of donors talk about their giving choices, and perhaps pool their money to invest, but decide individually where to donate. That would explain the eclectic list of colleges and the similar but not identical instructions they received.

“I could see a women’s giving circle … suggesting that it’s time for women to step up and fend for higher education at that level,” said Lauren Katzowitz Shenfield, principal of Philanthropy Advisors LLC in New York. But “I don’t get the anonymous piece.”

Experts were reluctant to throw out names. But several spoke generally about why donors give anonymously, and why some might even keep the recipient in the dark.

PRIVACY. Anonymous donations account for about 4 percent of $1 million-plus charitable gifts since 2000, according to Indiana University’s Center on Philanthropy. Associate executive director Dwight Burlingame said the top reason is to avoid getting hounded by other charities. But others include avoiding family conflicts over giving choices and personal safety, such as fear of kidnapping.

Why keep the identity even from the schools? Perhaps they don’t want to get hit up by the colleges for even more donations. Or they want to be extra sure that their identities remain secret. After all, anonymous donations don’t always stay anonymous. Word sometimes leaks through the fundraising grapevine. And in the early 1990s, the University of Toledo foundation had to give up anonymous donors’ names after a public records lawsuit from the local newspaper.

NOBILITY. In his famous “Ladder of Tzedakah,” the 12th-century Jewish philosopher Moses Maimonides ranked charitable acts in order of worthiness. Donations in which the recipient did not know the identity of the benefactor were considered especially admirable.

“It focuses attention on the good work of the `donee’ instead of focusing attention on the gifts of the donor,” said Dale, who previously headed the best-known charity that insisted on anonymity even from recipients – the Atlantic Philanthropies. That organization gave away over $2.5 billion during 20 years of anonymity before its backer – duty-free airport shop magnate Charles Feeney – was revealed in 1997.

SPARING THE COLLEGE. Ignorance of a gift’s source spares recipients not only chores like thank-you dinners, but also controversies over conflicts of interest or a donor’s politics.

FUN. “There’s a possibility they could be enjoying this,” Clemson’s O’Rourke said with a laugh. “They could really enjoy the world of education trying to figure out who these donors could be.”

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Associated Press reporters Amy Westfeldt in New York and Caryn Rousseau in Chicago contributed to this report.

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